Illustrative Application of the 2nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Point-Detector Response
This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response is the value of the model’s state function (particle concentration or particle flux) at a point in phase-space, which would simulate a pointwise measurement of the respective state function. This paradigm model admits exact closed-form expressions for all of the 1st- and 2nd-order response sensitivities to the model’s uncertain parameters and domain boundaries. These closed-form expressions can be used to verify the numerical results of production and/or commercial software, e.g., particle transport codes. Furthermore, this paradigm model comprises many uncertain parameters which have relative sensitivities of identical magnitudes. Therefore, this paradigm model could serve as a stringent benchmark for inter-comparing the performances of all deterministic and statistical sensitivity analysis methods, including the 2nd-CASAM.
References
[1]
Cacuci, D.G. (2020) Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework, AJCM, 10, 329-354.
[2]
Cacuci, D.G., Badea, A.F., Badea, M.C. and Peltz, J.J. (2016) Efficient Computation of Operator-Type Response Sensitivities for Uncertainty Quantification and Predictive Modeling: Illustrative Application to a Spent Nuclear Fuel Dissolver Model. International Journal for Numerical Methods in Fluids, 83, 149-174.
https://doi.org/10.1002/fld.4258
[3]
Cacuci, D.G. and Badea, M.C. (2018) Second-Order Adjoint Sensitivity Analysis of a Generic Evolution System with Applications to Radiation Transport and Fuel Reprocessing. PHYSOR-2018, Cancun, Mexico, April 22-26, 2018.
[4]
Cacuci, D.G. (2017) Inverse Predictive Modeling of Radiation Transport through Optically Thick Media in the Presence of Counting Uncertainties. Nuclear Science and Engineering, 186, 199-223. https://doi.org/10.1080/00295639.2017.1305244
[5]
Cacuci, D.G. and Favorite, J.A. (2018) Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses. Nuclear Science and Engineering, 190, 105-133. https://doi.org/10.1080/00295639.2018.1426899
[6]
Cacuci, D.G. (1981) Sensitivity Theory for Nonlinear Systems: I. Nonlinear Functional Analysis Approach. Journal of Mathematical Physics, 22, 2794-2802.
https://doi.org/10.1063/1.525186
[7]
Cacuci, D.G. (2020) Illustrative Application of the 2nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate Detector Response. AJCM, 10, 382-397.
